Suppose that there is a happy bug in the center of a circular water puddle. The bug is periodically shaking its legs in order to produce disturbances that travel through the water.

If these disturbances originate at a point, then they would travel outward from that point in all directions. Since each disturbance is traveling in the same medium, they would all travel in every direction at the same speed. The pattern produced by the bug's shaking would be a series of concentric circles. These circles would reach the edges of the water puddle at the same frequency.

An observer at point A (the left edge of the puddle) would observe the disturbances to strike the puddle's edge at the same frequency that would be observed by an observer at point B (at the right edge of the puddle). In fact, the frequency at which disturbances reach the edge of the puddle would be the same as the frequency at which the bug produces the disturbances. If the bug produces disturbances at a frequency of 2 per second, then each observer would observe them approaching at a frequency of 2 per second.

Now suppose that our bug is moving to the right across the puddle of water and producing disturbances at the same frequency of 2 disturbances per second. Since the bug is moving towards the right, each consecutive disturbance originates from a position that is closer to observer B and farther from observer A. Subsequently, each consecutive disturbance has a shorter distance to travel before reaching observer B and thus takes less time to reach observer B. Thus, observer B observes that the frequency of arrival of the disturbances is higher than the frequency at which disturbances are produced. On the other hand, each consecutive disturbance has a further distance to travel before reaching observer A. For this reason, observer A observes a frequency of arrival that is less than the frequency at which the disturbances are produced. The net effect of the motion of the bug (the source of waves) is that the observer towards whom the bug is moving observes a frequency that is higher than 2 disturbances/second; and the observer away from whom the bug is moving observes a frequency that is less than 2 disturbances/second. This effect is known as the Doppler effect.

  

 The Doppler Effect in Astronomy

Galaxies are clusters of stars that typically rotate about some center of mass point. Electromagnetic radiation emitted by such stars in a distant galaxy would appear to be shifted downward in frequency (a red shift) if the star is rotating in its cluster in a direction that is away from the Earth. On the other hand, there is an upward shift in frequency (a blue shift) of such observed radiation if the star is rotating in a direction that is towards the Earth. 

The relationship between source frequency f_s and detector frequency f_D can be determined by the following equation:

Where v is speed of sound, and v_s and v_d are the velocity of the sound source and sound detector respectively.

How to assign the signs in above equation?

• When source is moving toward the detector, use - for v_s (as this will make f_D larger)
• When source is moving away from the detector, use + for v_s (as this will make f_D smaller)
• When detector is moving toward the source, use + for v_d (as this will make f_D larger)
• When detector is moving away from the source, use - for v_s (as this will make f_D smaller)

Shock Waves and Sonic Booms

The Doppler effect is observed whenever the speed of the source is moving slower than the speed of the waves. But if the source actually moves at the same speed as or faster than the wave itself can move, a different phenomenon is observed.

If a moving source of sound moves at the same speed as sound, then the source will always be at the leading edge of the waves that it produces. The diagram at the right depicts snapshots in time of a variety of wavefronts produced by an aircraft that is moving at the same speed as sound. The circular lines represent compressional wavefronts of the sound waves. Notice that these circles are bunched up at the front of the aircraft. This phenomenon is known as a shock wave.

If you are standing on the ground when a supersonic (faster than sound) aircraft passes overhead, you might hear a very loud noise. This is called a “sonic boom”. A sonic boom occurs as the result of the piling up of compressional wavefronts. These compressional wavefronts pile up and interfere to produce a very high-pressure zone. Instead of these compressional regions (high-pressure regions) reaching you one at a time in consecutive fashion, they all reach you at once. Since every compression is followed by a rarefaction, the high-pressure zone will be immediately followed by a low-pressure zone. This creates a very loud noise.